What is the general solution for tan^3(x)=3tan(x) ?

The general solution for tan^3(x)=3tan(x) is x=pin,x=(2pi)/3+pin,x= pi/3+pin

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tan^3(x)=3tan(x)

tan^{3} (x) = 3 tan (x)

x = πn, x = \frac{2 π}{3} + πn, x = \frac{π}{3} + πn

Solution steps

tan^{3} (x) = 3 tan (x)

Solve by substitution

tan (x) = 0, tan (x) = - 3, tan (x) = 3

tan (x) = 0 : x = πn

tan (x) = - 3 : x = \frac{2 π}{3} + πn

tan (x) = 3 : x = \frac{π}{3} + πn

Combine all the solutions

x = πn, x = \frac{2 π}{3} + πn, x = \frac{π}{3} + πn

sin (2 x) = - cos (2 x)

3 sin (4 x) + 5 = 6

4 sin (x) + 3 = 0

tan (2 θ) = 3

cos (x) = 0.2

What is the general solution for tan^3(x)=3tan(x) ?
The general solution for tan^3(x)=3tan(x) is x=pin,x=(2pi)/3+pin,x= pi/3+pin